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In this paper we consider the problem of holomorphic continuation and removal of singularities of the CR functions given on ΓK, where Γ is a generic manifold with nondegenerate Levi form and K is a meromorphically p-convex compactum. We get some conditions on Γ, relative to p-convexity and q-concavity, under which every integrable CR function given on ΓK extends holomorphically in some domain ΩΓ\K, where ΩΓ is a wedge domain with edge Γ. Our Results are local.